The Argentine international, who made 52 league appearances for Manchester United from 2004-07, has been linked with both Tottenham Hotspur and Liverpool in the past, and is being tipped to leave the Spanish capital during the close season as the Madridistas splash out on new recruits.
And it is the North London outfit who are believed to have stolen a march on their rivals by holding talks with the Argentine international.
Spurs, who have been linked to a string of Real Madrid players this summer - including Ruud van Nistelrooy, Klaas-Jan Huntelaar and Arjen Robben - are keen to land an established left-back with Gareth Bale having struggled to make an impression and Benoit Assou-Ekotto failing to convince the Spurs faithful.
And Heinze has revealed he would be open to a return to top flight English football.
"I would not mind playing Premier League football again, I am aware that several clubs are interested, but I must speak with Real Madrid first," he told Telam.
"I have no idea of where I am going to end up and I am yet to think about my future.
"I have a contract with Real Madrid and you have to have a professional attitude."
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